To prove by induction that 8+5+2…+(11-3n) = (1/2)(19n-3n^2) is true for all positive integers n, we assume 8+5+2…+(11-3k) = (1/2)(19k-3k^2)…

To prove by induction that 8+5+2…+(11-3n) = (1/2)(19n-3n^2) is true for all positive integers n, we assume 8+5+2…+(11-3k) = (1/2)(19k-3k^2) is true for some positive integer k, and show that 8+5+2…+(11-3k) + (11-3(k+1)) = A where A is